There are three ways to deal with enemy culture.  In the long-run, your only permanent option is culture of your own.  You can also slow the spread of enemy culture by stationing capital ships in friendly planets.  Against small amounts of culture, this can stop its advance completely.  The final solution is to go out and find the enemy culture stations and destroy them.  That's the most aggressive solution and can be very effective if you're running a pure military setup, but requires you to have superior firepower (so the enemy fleet can't stop you) or superior mobility (so you can get in and get the job done before they can react).